def con2vert(A, b):
"""
Convert sets of constraints to a list of vertices (of the feasible region).
If the shape is open, con2vert returns False for the closed property.
"""
# Python implementation of con2vert.m by Michael Kleder (July 2005),
# available: http://www.mathworks.com/matlabcentral/fileexchange/7894
# -con2vert-constraints-to-vertices
# Author: Michael Kelder (Original)
# Andre Campher (Python implementation)
c = linalg.lstsq(mat(A), mat(b))[0]
btmp = mat(b)-mat(A)*c
D = mat(A)/matlib.repmat(btmp, 1, A.shape[1])
fmatv = qhull(D, "Ft") #vertices on facets
G = zeros((fmatv.shape[0], D.shape[1]))
for ix in range(0, fmatv.shape[0]):
F = D[fmatv[ix, :], :].squeeze()
G[ix, :] = linalg.lstsq(F, ones((F.shape[0], 1)))[0].transpose()
V = G + matlib.repmat(c.transpose(), G.shape[0], 1)
ux = uniqm(V)
eps = 1e-13
Av = dot(A, ux.T)
bv = tile(b, (1, ux.shape[0]))
closed = sciall(Av - bv <= eps)
return ux, closed
def vert2con(V):
"""
Convert sets of vertices to a list of constraints (of the feasible region).
Return A, b and s of the set; Ax < b (s is the sign-vector [to be used later])
vert2con always closes the shape and generates inequalities accordingly.
"""
# Dependencies: * qhull (libqhull5, qhull-bin)
# * scipy
k = qhull(V,"n") #convert to martrix with vertices
# k is a (n+1)x(p) matrix in the form [A b] (from qhull doc: Ax < -b is
# satisfied), thus;
A = k[:, :-1]
b = array([-k[:, -1]]).T
s = -ones(b.shape)
return A, s, b
def tryvol(A, b, cs):
"""
Try to determine volume of feasible region, otherwise impose box
constraint.
"""
try:
V = con2vert(A, b)[0] # get vertices for constraint set iteration
except NameError: #catch unbound shapes
#create large box around original shape
fixA = r_[eye(cs.nd), -eye(cs.nd)]
fixb = r_[[numpy.max(cs.vert[:, x]) for x in range(cs.vert.shape[1])],
[-numpy.min(cs.vert[:, x]) for x in range(cs.vert.shape[1])]]
fixb = array([fixb]).T
fA = r_[fixA, A]
fb = 2. * r_[fixb, b] # double the box size
V = con2vert(fA, fb)[0]
#return vol (normal or fixed) and vertices (normal or fixed)
return qhull(V, "FS"), V
def vol(self):
"""Return 'volume' of feasible region."""
return qhull(self.vert,"FS")